可修系统不完全维修连续比例强度模型及应用

Imperfect repair continuous proportional intensity model for repairable systems and its application

为解决传统不完全维修模型难于工程应用的问题,基于边界强度过程理论,提出一种新的具有封闭形式解的连续比例强度模型。讨论模型的特性,推导模型参数及诸如给定时刻的条件可靠度、期望故障数、累积平均故障间隔时间等重要可靠性指标的极大似然点估计的计算公式,利用Fisher信息矩阵法和delta法给出模型参数及上述可靠性指标的区间估计,基于Akaike信息准则和拟合优度检验指标R,给出模型评价准则。以数控机床现场故障数据为例对所提方法进行验证。研究结果表明:应用本文方法可以获得数控机床可靠性指标封闭形式的解及置信区间,可以很好地应用于工程实际。

Considering that traditional imperfect repair model was difficult to use in practice, a new continuous proportional intensity model with closed-form solutions was proposed based on the theory of bounded intensity process. The characteristics of the model were discussed, the formula of point maximum likelihood estimators for model parameters, as well as the important reliability indices such as the conditional reliability at given time, the s-expected number of failures, and the cumulative mean time between failure were all derived, the interval estimators of model parameters and reliability indices were given by using the Fisher information matrix method and delta method, and the assessment criterion of model was provided based on Akaike information criterion and the index of goodness-of-fit test. An example of real failure data from numerical control machine tools was taken to prove the proposec~ method. The results show that the closed-form solutions and confidence bounds of reliability indices for NC machine tools are obtained and the method can be well applied in practical.